Generalized Rosenfeld scalings for tracer diffusivities in not-so- simple fluids: Mixtures and soft particles
William P. Krekelberg, Mark J. Pond, Gaurav Goel, Vincent K. Shen, Jeffrey R. Errington, Thomas M. Truskett
Rosenfeld [Phys. Rev. A 15, 2545 (1977)] originally noticed that casting the transport coefficients of simple monatomic, equilibrium fluids in a specific dimensionless form makes them approximately single-valued functions of excess entropy. This observation has predictive value because, while the transport coefficients of dense fluids can be difficult to estimate from first principles, the excess entropy can often be accurately predicted from liquid-state theory. In this work, we use molecular simulations to investigate whether Rosenfeld s observation is a special case of a more general scaling law relating the tracer diffusivities of particles in mixtures to the excess entropy. Specifically, we study the tracer diffusivities, static structure, and thermodynamic properties of a variety of one- and two-component model fluid systems with either additive or non- additive interactions of the hard-sphere or Gaussian-core form. The results of the simulations demonstrate that the effects of mixture concentration and composition, particle-size asymmetry and addivity, and strength of the interparticle interactions in these fluids are consistent with an empirical scaling law relating the excess entropy to a new dimensionless (generalized Rosenfeld) form of tracer diffusivity, which we introduce here. The dimensionless form of the tracer diffusivity follows from knowledge of the intermolecular potential and the transport/thermodynamic behavior of fluids in the dilute limit. The generalized Rosenfeld scaling requires less information, and provides more accurate predictions, than either Enskog theory or scalings based on the pair-correlation contribution to the excess entropy. As we show, however, it also suffers from some limitations, especially for systems that exhibit significant decoupling of individual component tracer diffusivities.
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)